Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
On the Computation of Square Roots in Finite Fields
Designs, Codes and Cryptography
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Integer Variable Χ---Based Ate Pairing
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Discrete Applied Mathematics
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Faster Pairings on Special Weierstrass Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Fast Hashing to G2 on Pairing-Friendly Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
How to Hash into Elliptic Curves
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Faster $\mathbb{F}_p$-Arithmetic for Cryptographic Pairings on Barreto-Naehrig Curves
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Efficient and generalized pairing computation on Abelian varieties
IEEE Transactions on Information Theory
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
Improved generalized Atkin algorithm for computing square roots in finite fields
Information Processing Letters
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
Aggregate and verifiably encrypted signatures from bilinear maps
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
On compressible pairings and their computation
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
IEEE Transactions on Information Theory
New software speed records for cryptographic pairings
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Constructing tower extensions of finite fields for implementation of pairing-based cryptography
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
An analysis of affine coordinates for pairing computation
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
High-speed software implementation of the optimal ate pairing over Barreto-Naehrig curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Faster explicit formulas for computing pairings over ordinary curves
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Efficient and provably-secure identity-based signatures and signcryption from bilinear maps
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Improved signcryption from q-Diffie-Hellman problems
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Faster pairing computations on curves with high-degree twists
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
IEEE Transactions on Information Theory
Implementing cryptographic pairings over barreto-naehrig curves
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Faster explicit formulas for computing pairings over ordinary curves
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
FPGA implementation of pairings using residue number system and lazy reduction
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Non-interactive distributed encryption: a new primitive for revocable privacy
Proceedings of the 10th annual ACM workshop on Privacy in the electronic society
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Parallelizing the weil and tate pairings
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
On the efficient implementation of pairing-based protocols
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Attractive subfamilies of BLS curves for implementing high-security pairings
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Indifferentiable hashing to barreto---naehrig curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
SMSCrypto: A lightweight cryptographic framework for secure SMS transmission
Journal of Systems and Software
Core based architecture to speed up optimal ate pairing on FPGA platform
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Implementing pairings at the 192-bit security level
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Speeding up ate pairing computation in affine coordinates
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
A more efficient computationally sound non-interactive zero-knowledge shuffle argument
Journal of Computer Security - Advances in Security for Communication Networks
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Abstract: For the last decade, elliptic curve cryptography has gained increasing interest in industry and in the academic community. This is especially due to the high level of security it provides with relatively small keys and to its ability to create very efficient and multifunctional cryptographic schemes by means of bilinear pairings. Pairings require pairing-friendly elliptic curves and among the possible choices, Barreto-Naehrig (BN) curves arguably constitute one of the most versatile families. In this paper, we further expand the potential of the BN curve family. We describe BN curves that are not only computationally very simple to generate, but also specially suitable for efficient implementation on a very broad range of scenarios. We also present implementation results of the optimal ate pairing using such a curve defined over a 254-bit prime field.